This blog is about statistics, evolution, nutrition, lifestyle, and health issues. A combination of these issues. The focus is on quantitative research and how it can be applied in practice. But you may see other types of posts here (e.g., recipes, ideas, concepts, theories) from time to time.

Monday, March 19, 2012

I am not a big fan of using arguments such as “food questionnaires are unreliable” and “observational studies are worthless” to completely dismiss a study. There are many reasons for this. One of them is that, when people misreport certain diet and lifestyle patterns, but do that consistently (i.e., everybody underreports food intake), the biasing effect on coefficients of association is minor. Measurement errors may remain for this or other reasons, but regression methods (linear and nonlinear) assume the existence of such errors, and are designed to yield robust coefficients in their presence. Besides, for me to use these types of arguments would be hypocritical, since I myself have done several analyses on the China Study data (), and built what I think are valid arguments based on those analyses.

My approach is: Let us look at the data, any data, carefully, using appropriate analysis tools, and see what it tells us; maybe we will find evidence of measurement errors distorting the results and leading to mistaken conclusions, or maybe not. With this in mind, let us take a look at the top part of Table 3 of the most recent (published online in March 2012) study looking at the relationship between red meat consumption and mortality, authored by Pan et al. (Frank B. Hu is the senior author) and published in the prestigious Archives of Internal Medicine (). This is a prominent journal, with an average of over 270 citations per article according to Google Scholar. The study has received much media attention recently.

Take a look at the area highlighted in red, focusing on data from the Health Professionals sample. That is the multivariate-adjusted cardiovascular mortality rate, listed as a normalized percentage, in the highest quintile (Q5) of red meat consumption from the Health Professionals sample. The non-adjusted percentages are 1.4 percent mortality in Q5 and 1.13 in Q1 (from Table 1 of the same article); so the multivariate adjustment-normalization changed the values of the percentages somewhat, but not much. The highlighted 1.35 number suggests that for each group of 100 people who consumed a lot of red meat (Q5), when compared with a group of 100 people who consumed little red meat (Q1), there were on average 0.35 more deaths over the same period of time (more than 20 years).

The heavy red meat eaters in Q5 consumed 972.37 percent more red meat than those in Q1. This is calculated with data from Table 1 of the same article, as: (2.36-0.22)/0.22. In Q5, the 2.36 number refers to the number of servings of red meat per day, with each serving being approximately 84 g. So the heavy red meat eaters ate approximately 198 g per day (a bit less than 0.5 lb), while the light red meat eaters ate about 18 g per day. In other words, the heavy red meat eaters ate 9.7237 times more, or 972.37 percent more, red meat.

So, just to be clear, even though the folks in Q5 consumed 972.37 percent more red meat than the folks in Q1, in each matched group of 100 you would not find a single additional death over the same time period. If you looked at matched groups of 1,000 individuals, you would find 3 more deaths among the heavy red meat eaters. The same general pattern, of a minute difference, repeats itself throughout Table 3. As you can see, all of the reported mortality ratios are 1-point-something. In fact, this same pattern repeats itself in all mortality tables (all-cause, cardiovascular, cancer). This is all based on a multivariate analysis that according to the authors controlled for a large number of variables, including baseline history of diabetes.

Interestingly, looking at data from the same sample (Health Professionals), the incidence of diabetes is 75 percent higher in Q5 than in Q1. The same is true for the second sample (Nurses Health), where the Q5-Q1 difference in incidence of diabetes is even greater - 81 percent. This caught my eye, being diabetes such a prototypical “disease of affluence”. So I entered the whole data reported in the article into HCE () and WarpPLS (), and conducted some analyses. The graphs below are from HCE. The data includes both samples – Health Professionals and Nurses Health.

HCE calculates bivariate correlations, and so does WarpPLS. But WarpPLS stores numbers with a higher level of precision, so I used WarpPLS for calculating coefficients of association, including correlations. I also double-checked the numbers with other software, just in case (e.g., SPSS and MATLAB). Here are the correlations calculated by WarpPLS, which refer to the graphs above: 0.030 for red meat intake and mortality; 0.607 for diabetes and mortality; and 0.910 for food intake and diabetes. Yes, you read it right, the correlation between red meat intake and mortality is a very low and non-significant 0.030 in this dataset. Not a big surprise when you look at the related HCE graph, with the line going up and down almost at random. Note that I included the quintiles data from both the Health Professionals and Nurses Health samples in one dataset.

Those folks in Q5 had a much higher incidence of diabetes, and yet the increase in mortality for them was significantly lower, in percentage terms. A key difference between Q5 and Q1 being what? The Q5 folks ate a lot more red meat. This looks suspiciously suggestive of a finding that I came across before, based on an analysis of the China Study II data (). The finding was that animal food consumption (and red meat is an animal food) was protective, actually reducing the negative effect of wheat flour consumption on mortality. That analysis actually suggested that wheat flour consumption may not be so bad if you eat 221 g or more of animal food daily.

So, I built the model below in WarpPLS, where red meat intake (RedMeat) is hypothesized to moderate the relationship between diabetes incidence (Diabetes) and mortality (Mort). Below I am also including the graphs for the direct and moderating effects; the data is standardized, which reduces estimation error, particularly in moderating effects estimation. I used a standard linear algorithm for the calculation of the path coefficients (betas next to the arrows) and jackknifing for the calculation of the P values (confidence = 1 – P value). Jackknifing is a resampling technique that does not require multivariate normality and that tends to work well with small samples; as is the case with nonparametric techniques in general.

The direct effect of diabetes on mortality is positive (0.68) and almost statistically significant at the P < 0.05 level (confidence of 94 percent), which is noteworthy because the sample size here is so small – only 10 data points, 5 quintiles from the Health Professionals sample and 5 from the Nurses Health sample. The moderating effect is negative (-0.11), but not statistically significant (confidence of 61 percent). In the moderating effect graphs (shown side-by-side), this negative moderation is indicated by a slightly less steep inclination of the regression line for the graph on the right, which refers to high red meat intake. A less steep inclination means a less strong relationship between diabetes and mortality – among the folks who ate the most red meat.

Not too surprisingly, at least to me, the results above suggest that red meat per se may well be protective. Although we should consider a least two other possibilities. One is that red meat intake is a marker for consumption of some other things, possibly present in animal foods, that are protective - e.g., choline and vitamin K2. The other possibility is that red meat is protective in part by displacing other less healthy foods. Perhaps what we are seeing here is a combination of these.

Whatever the reason may be, red meat consumption seems to actually lessen the effect of diabetes on mortality in this sample. That is, according to this data, the more red meat is consumed, the fewer people die from diabetes. The protective effect might have been stronger if the participants had eaten more red meat, or more animal foods containing the protective factors; recall that the threshold for protection in the China Study II data was consumption of 221 g or more of animal food daily (). Having said that, it is also important to note that, if you eat excess calories to the point of becoming obese, from red meat or any other sources, your risk of developing diabetes will go up – as the earlier HCE graph relating food intake and diabetes implies.

Please keep in mind that this post is the result of a quick analysis of secondary data reported in a journal article, and its conclusions may be wrong, even though I did my best not to make any mistake (e.g., mistyping data from the article). The authors likely spent months, if not more, in their study; and have the support of one of the premier research universities in the world. Still, this post raises serious questions. I say this respectfully, as the authors did seem to try their best to control for all possible confounders.

I should also say that the moderating effect I uncovered is admittedly a fairly weak effect on this small sample and not statistically significant. But its magnitude is apparently greater than the reported effects of red meat on mortality, which are not only minute but may well be statistical artifacts. The Cox proportional hazards analysis employed in the study, which is commonly used in epidemiology, is nothing more than a sophisticated ANCOVA; it is a semi-parametric version of a special case of the broader analysis method automated by WarpPLS.

Finally, I could not control for confounders because, given the small sample, inclusion of confounders (e.g., smoking) leads to massive collinearity. WarpPLS calculates collinearity estimates automatically, and is particularly thorough at doing that (calculating them at multiple levels), so there is no way to ignore them. Collinearity can severely distort results, as pointed out in a YouTube video on WarpPLS (). Collinearity can even lead to changes in the signs of coefficients of association, in the context of multivariate analyses - e.g., a positive association appears to be negative. The authors have the original data – a much, much larger sample - which makes it much easier to deal with collinearity.

Moderating effects analyses () – we need more of that in epidemiological research eh?

43 comments:

Anonymous
said...

"The highlighted 1.35 number suggests that for each group of 100 people who consumed a lot of red meat (Q5), when compared with a group of 100 people who consumed little red meat (Q1), there were on average 0.35 more deaths over the same period of time (more than 20 years)."

I thought that it meant that with the mortality rate normalized at 1 for the first group, the 1.35 meant that the mortality rate was 35% higher for the other group.

What you said is correct too Anon. And illustrates one of my points in this post, but not my main point. The way findings are stated can sound more or less ominous. The way you stated one of the findings sounds more ominous than the way I stated.

Hi David. Getting the original dataset for a study like this would be very difficult. Requests are usually ignored. Open records requests are not very effective – they can be fulfilled with messy paper-based records that are worthless.

Hi Anon. The reasons are that: (a) the correlation (unadjusted) between red meat intake and mortality is practically zero; and (b) a higher incidence of diabetes is expected to be associated with an increase in mortality rate, which is the case here (correlation = 0.607).

You said: "when people misreport certain diet and lifestyle patterns, but do that consistently (i.e., everybody underreports food intake), the biasing effect on coefficients of association is minor". I believe the point of Denis Meninger analysis was that people do not under report meat consumption consistently. Health conscious people underreport and non-health conscious people in fact overreport meat consumption (the Australian study)

Hi Miki. My comment was not aimed at anyone in particular, other than myself I guess. Like any human being (I think), I have the temptation to claim that a result that I don’t think is “real” or reasonable is due to a mistake of some kind – e.g., measurement error.

It is harder work, but it seems to always make more sense to take a hard look at the data, and see what it actually tells us. Not very easy with secondary data from articles, but can be done. If measurement error is biasing the results, then we should see evidence of other “odd” effects.

Btw, if some people underreport and others overreport, in close to equal numbers, the regression line or curve that will be used to estimate an effect will pass through the resulting points, somewhere around the “middle”. The errors should not influence it that much.

That is not to say that errors should be ignored. If we had found things like “diabetes is protective”, or something else that was “odd”, then we might have been able to trace the results back to measurement error. But most of the correlations here seem reasonable.

I have an idea for the actual reason why the authors of the study found that red meat intake increases mortality, but I need more time to think about it. It is somewhat technical. I don't think they simply "lied".

Btw, mortality may well be one of the most reliably measured variables in this study. Either one is dead or not. So if folks were misreporting consumption of red meat, and those folks were health professionals (among whom the lipid hypothesis is still king), my guess is that they would have underreported in a way that was inversely proportional to their actual intake of red meat. That is, those who eat little (Q1) would not underreport as much as those who eat a lot (Q5).

How interesting eh? This would mean that the gap in actual (as opposed to reported) intake between Q5-Q1 would be wider. As the data currently stands, the gap is already close to 1,000 percent.

If red meat were so bad for one’s health, how would it be possible that such a large gap would lead to only 3 additional deaths per 1,000 people?

You are absolutely right David. What I meant to say was “disease of civilization”, or something that would convey the idea that diabetes is a disease that is largely caused by modern diet-lifestyle patterns.

As it happens, in urban areas today the poor tend to generally gravitate toward the most harmful consumption patterns of modern industrialized foods.

A statistics question for you... one blogger pointed out that another observational study published by the same group came out looking at sugar consumption and the incidence of CVD. Link http://circ.ahajournals.org/content/early/2012/03/09/CIRCULATIONAHA.111.067017.full.pdf+html

The question I have is why one would choose to look at quintiles in the red meat study and quartiles in the sugar study? Do researchers slice and dice the numbers and cherry pick the tertiles, quartiles, or quintiles which make the most compelling statistical correlations?

When would it be appropriate (from a statistical sense) to look at quartiles, versus quintiles, versus not bucketing groups at all?

back to the very first comment... if you normalize the mortality of the lowest red meat consumption quintile at 1.0, and the highest meat consumption mortality rate is 1.35, how can you say there are are .35 more deaths per 100? That would imply that the mortality rate for the lowest group is 1 per 100, and that doesnt seem to be the case, since that number is normalized.

Often the adjustment-normalization process widens the gap a bit, in terms of the magnitude of the effect (35 percent), when compared with the non-adjusted-normalized values. The latter in this case would be (1.4-1.13)/1.13 = 23.89 percent.

I don’t like the normalization (or re-scaling) either. Starting at 1 percent for each variable/model takes out information that would be useful to some folks, although it may make it easier for nontechnical readers to visualize what is going on.

A hazard ratio is independent of time. It does not mean, as you say, that, "there were on average 0.35 more deaths over the same period of time (more than 20 years)." A hazard ratio is independent of time.

The number needed to treat (if the treatment is reducing red meat intake) is 286.

That's equivalent to the following scenario:

I give you 286 tablets. One is poisonous and will certainly kill you if you take it.

At some point in the next 20 years, you will receive a phone call and have to take 1 of the tablets and throw out the rest.

The phone call could come tomorrow, or any time in the next 20 years.

By eating 2 or more servings of red meat per day, you are essentially subjecting yourself to what I described above.

"The highlighted 1.35 number suggests that for each group of 100 people who consumed a lot of red meat (Q5), when compared with a group of 100 people who consumed little red meat (Q1), there were on average 0.35 more deaths over the same period of time (more than 20 years)."

I thought that it meant that with the mortality rate normalized at 1 for the first group, the 1.35 meant that the mortality rate was 35% higher for the other group.

This person has a point, which you never fully responded to.

The NNT statistic is not perfect, as I said, but it is a far more accurate way to represent the number of people who are at risk with the treatment versus without the treatment than your misunderstanding.

The NNT with respect to Q5-Q1 is essentially the number of people that would have to be “treated” to bring the mortality rate in Q5 down to the mortality rate in Q1.

Since you are talking about red meat as a “poison”, what you have in mind is probably something else - acronym NNH.

This all takes an ANCOVA-like view of the situation; that is, one key independent variable needs to be manipulated, and that’s all. The target being red meat.

WarpPLS is a multivariate data analysis tool that assesses multiple independent-dependent variable relationships at the same time. Like ANCOVA, it allows for covariates, but does much more than that.

In the context of a WarpPLS analysis, it would be more correct to say that a certain variation in variable RM (number of servings of RM) leads to a certain increase in mortality (M), when the effects of variables X, Y, Z etc. are controlled for.

Moreover, ANCOVA and variations, such as the Cox proportional hazards analysis, are parametric analysis methods that make some “hard” assumptions about the data – e.g., that it is normally distributed.

So, I can see (barely), what you mean when invoking NNT, but we are talking about very different things here. I also included the results of a basic moderating effect analysis to illustrate my point.

You are right to say that I was out of line telling you to read a "basic statistics textbook." Of course, you are more knowledgeable about statistics than all but a handful of people.

It's difficult for a person who has that knowledge to communicate with the public in a way they understand.

Sorry about oversimplifying the data. I do understand, now, that it isn't possible to simply conclude that red meat was the cause. I simply trusted that the authors did an appropriate sensitivity analysis. I see, now, that that was not the case.

What you say makes sense. I understand that total calories may matter more in whether or not people develop diabetes.

However, I'm not convinced that red meat is helpful in reducing mortality from cancer. The evidence I have seen includes a large study from 2008 that showed an association between cancer and red meat intake.

Btw, in discussions of red meat intake’s effect on health, often iron overload is mentioned. What many people don’t seem to realize is that iron overload is caused primarily by hereditary haemochromatosis. Another cause are frequent transfusions with the goal of improving athletic performance.

Hereditary haemochromatosis is a rare genetic disorder. Transfusions with the goal of improving athletic performance, or “blood doping”, seem to have been historically common among elite cyclists.

"3) Vegetarian diets virtually eliminate the possibility of having a myocardial infarction."

Where on earth did you get that supposed factoid?

Denise Minger has a nice discussion of meat and cardiovascular disease:

http://rawfoodsos.com/2011/01/06/vegetarians-and-heart-disease/

Incidentally, I have been a vegetarian for 44 years. It is possible to eat healthily as a vegetarian, but it is equally possible to eat unhealthily.

I find that a lot of vegetarians ultimately end up gaining weight and moving in the direction of Type II diabetes. I was well down that road. The message that I needed to turn things around was a blood pressure reading of 183/114 and sky-high triglycerides. I certainly think I was a candidate for a heart attack--even though at the time I hadn't had a bite of meat in 41 years.

I'm still a vegetarian. And I think that most factory-farmed meat contains many dangers (especially in the form of anitbiotics and growth hormones). But I think there are just as many dangers on the cereal or chips aisles of a supermarket.

It's just a good idea not to eat industrial crap, animal or otherwise.

Ned Kock

About Me

I strongly believe that lifestyle, nutrition and exercise habits that are compatible with our evolutionary past are the key to optimal health. On the other hand, I do not believe that closely mimicking life in the Paleolithic is optimal for health, or even viable. I am a researcher, software developer, consultant, and college professor. Two of my main areas of research are nonlinear variance-based structural equation modeling, and evolutionary biology as it applies to the study of human-technology interaction. My degrees are in engineering (B.E.E.), computer science (M.S.), and business (Ph.D.). I am interested in the application of science, statistics, and technology to the understanding of human health and behavior. I blog about evolution, health, statistics, and technology. My personal web site contains links to my contact information and freely available articles related to the topics of my blogs: nedkock.com.

Copyright

The contents of this blog may be used with proper attribution. This blog makes limited use of copyrighted material (including tables and figures) for commentary, always with proper attribution and in ways that comply with fair use law.